Phenomenal consciousness, or `P-consciousness' for short, is \what it's like" consciousness; Block (1995) provides a nice description thereof. E.g., there's something it's like to taste a glorious Burgundian red wine, carve a ski turn at high speed, etc. There's also something it's like to be you, and something it's like to be us. P-consciousness is rather hard to formalize, to put it mildly; for this reason, some have claimed that any dedicated attempt to build a P-conscious machine is a non-starter, at least at present Bringsjord (2007). Cognitive consciousness, on the other hand, are those states of an agent that involve its knowing, believing, intending, desiring, perceiving, fearing, communicating, : : : only structurally and computationally speaking, with not even the slightest nod in the direction of \raw feels" or \qualia." Remark: While we have no doubt that phenomenal consciousness has great practical value, there can also be little doubt that it's not exactly easy to put one's nger on what its value is; this is especially true if one is searching for its value from an evolutionary perspective Bringsjord et al. (2002). Cognitive consciousness stands in stark contrast to this situation, for even in the case of
In this brief work-in-progress document we introduce , a new and novel
framework for measuring cognitive consciousness that stands in dramatic contrast
with the longstanding of
The foundation for
consists in four parts, to wit:
1. Cognitive Calculi. This is an in nite space of what might fairly be termed
\cognitive logics" that roughly coincides with a family of multi-operator
higher-order2 quanti ed modal logics. One sub-family of the space is DCE C ,
which anchors the example given below, and whose typed signature, and
inference schemata, are given e.g. in Govindarajulu & Bringsjord (2017a).
2. The Axiom System CA. An initial, formal axiomatization of cognitive
consciousness has been achieved, via the axiom system CA given in Bringsjord,
Bello & Govindarajulu (2018); this system is expressed in a cognitive
calculus.
3. ShadowProver (the reasoner). Bringing arti cial agents to (cognitively)
conscious life is enabled by an automated theorem-proving system able to handle
the highly expressive nature of cognitive calculi: viz., ShadowProver
(Govindarjaulu 2017).3
4. Spectra (the planner). Arti cial agents plan to achieve their goals and desires
through Spectra
On
The Basic Idea: provides a measure of the degree of cognitive consciousness for an agent at a time (and over intervals composed of such times), and does so by rst appropriating standard = = measures of the complexity of purely extensional formulae in logics like rst- and second-order logic.5 From there, 2 For cognoscenti, it would be more accurate to say that the extensional component of cognitive calculi are generally n-order, where 0 n 3. 3 The novel technique of shadowing, which allows for great e ciency of proof-search, is out of scope here. The prover is available at: https://github.com/naveensundarg/prover. 4 The planner is available at: https://github.com/naveensundarg/Spectra. 5 While we can explain in person from scratch at the symposium with slides, cognoscenti can immediately get an informative sense of by being told that e.g. operators are allowed to entire the picture, and tracks and measures complexity that arises from this. An example follows.
Example Consciousness and the Doctrine of Double E ect Figure 1 shows how
measures cognitive consciousness in an agent that is in the process of
computing the Doctrine of Double E ect (DDE)
Applied to Single Chunk & Time of Conscious Agent 5
Here are some properties of the
framework of potential interest to our readers: Non-Binary Whereas is such that an agent either is or is not (P-) conscious, cognitive consciousness as measured by admits of a ne-grained range of the degree of cognitive consciousness.
Zero for Some Animals and Machines Animals such as insects, and computing machines that are end-to-end statistical/connectionist \ML," have zero , and hence cannot be cognitively conscious. In contrast, as emphasized to Bringsjord in personal conversation,7 says that even lower animals are conscious.
Human-Nonhuman Discontinuity Explained by From the computational/AI point of view, cognitive scientists have taken note of a severe discontinuity between H. sapiens sapiens and other biological creatures on Earth (Penn et al. 2008), and the sudden and large jump in level of from (say) chimpanzees and dolphins to humans is in line with this observation. It's for instance doubtful that any nonhuman animals are capable of reaching thirdorder belief; hence [B; 0] = n, where n 3, for any nonhuman animal, is impossible. In stark contrast, each of us believes that you, the reader, believe that we believe that Palo Alto is located in California. where is 3 (e.g., the formal de nition of a limit in the di erential/integral calculus), an agent a who knows that another agent a0 knows at some time t, where this is the sum total of the cognitive activity of a, has by this alone a level of that is [K; 1] = 3. See the appendix for more details. 6 The principle is worth studying from the perspective of cognitive science, as there have been empirical studies that humans employ this principle. 7 With Tononi and C. Koch, SRI T&C Series. Human-Human Discontinuity Explained by A given neurobiologically normal human, over the course of his or her lifetime, has very di erent cognitive capacity. E.g., it's well-known that such a human, before the age of four or ve, is highly unlikely to be able to solve what has become known as the false-belief task (or sometimes the sally-anne task ), which we can denote by `FBT.' From the point of view of , the explanation is simply that an agent with insu ciently high cognitive consciousness is incapable of solving such a task; speci cally, solving FBT requires an agent to have beliefs about the beliefs of other agents, where the target of those beliefs involves at least basic quanti cation.8 Non-existent Agents Can Have Cognitive Consciousness In fact, such agents can have high levels of cognitive consciousness. For example, brilliant ctional detectives, such as Poe's remarkable C. Auguste Dupin, can be shown to have high levels of cognitive consciousness. E.g., in \The Purloined Letter" Dupin exploits his ability to infer what logic dictates he should believe about the criminal's beliefs about the beliefs of detectives investigating said detective. 6
AIs based purely on statistical/connectionist \machine learning" of the contemporary sort (e.g., \deep learning") would appear to have no cognitive consciousness whatsoever, for the simple reason that arguments to can't be found in such arti cial agents.9 We expect resistance from proponents of today's ML, and look forward to discussion and debate. 7
We have reached the point, in the relevant line of work, at which we can provide some interesting theorems regarding the framework, and can, courtesy of implementation enabled by ShadowProver, demonstrate cognitively conscious machines. We will provide some demonstrations at the symposium itself, by which time we expect these demonstrations, and the body of formal results underlying them, to be rather robust. 8
The invention and re nement of cognitive calculi has been in part enabled by
generous and longstanding support from AFOSR to the RAIR Lab. The
invention and re nement of cognitive calculi that allow an AI to engage speci cally
8 An arti cial agent able to solve FBT is presented by
URL: http://kryten.mm.rpi.edu/SB PB NSG TowardAxiomatizingConsciousness o print.pdf
for a given system is de ned as a function from modal operators M = fB; K; I; D; O; : : :g (denoting a range of cognitive states in a cognitive calculus) and natural numbers to natural numbers: : M N ! N: The cognitive states we usually consider include, but are not limited to, beliefs B, knowledge K, intentions I, desires D, and obligations O. A part of the speci cation is given below:
Intensional Complexity of Representations/Formulae [B; 0] = maximum intensional complexity of beliefs [K; 0] = maximum intensional complexity of knowledge [I; 0] = maximum intensional complexity of intensions [D; 0] = maximum intensional complexity of desires [O; 0] = maximum intensional complexity of obligations . .
.
Quanti cational Complexity of Representations/Formulae [B; 1] = n (in.ew., hmeraexiwmeuhmavqeuBan(ti)caantdionailsdeeipththerof nb=elienfs [K; 1] = maximum quanti cational depth of knowledge [I; 1] = maximum quanti cational depth of intensions [D; 1] = maximum quanti cational depth of desires [O; 1] = maximum quanti cational depth of obligations . .
.
Extensional Complexity of Representations/Formulae [B; 2] = maximum extensional depth of belief [K; 2] = maximum extensional depth of knowledge [I; 2] = maximum extensional depth of intension [D; 2] = maximum extensional depth of desire [O; 2] = maximum extensional depth of obligation . .
.
Time Complexity of Representations/Formulae [B; 3] = Maximum di erence between time expressions within beliefs [K; 3] = Maximum di erence between time expressions within knowledge [I; 3] = Maximum di erence between time expressions within intensions [D; 3] = Maximum di erence between time expressions within desires [O; 3] = Maximum di erence between time expressions within obligations . . .